A363350 - OEIS

%I #13 Nov 19 2023 08:25:34

%S 1,1,16,51,276,969,3504,10659,30954,81719,205040,482885,1088100,

%T 2340135,4850640,9694845,18789795,35357670,64833120,115997970,

%U 203014680,347993910,585292320,966955410,1571349780,2514084066,3964589856,6167026726,9470900056,14369476066,21554373984

%N Number of n element multisets of length 4 vectors over GF(2) that sum to zero.

%C a(n) is the number of n X 4 binary matrices under row permutations and column complementations.

%C See A362905 for other interpretations.

%H Andrew Howroyd, <a href="/A363350/b363350.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (8, -20, -8, 126, -168, -196, 680, -239, -1072, 1240, 560, -1820, 560, 1240, -1072, -239, 680, -196, -168, 126, -8, -20, 8, -1).

%F G.f.: (1 - 7*x + 28*x^2 - 49*x^3 + 70*x^4 - 49*x^5 + 28*x^6 - 7*x^7 + x^8)/((1 - x)^16*(1 + x)^8).

%F a(n) = binomial(n+15, 15)/16 for odd n;

%F a(n) = (binomial(n+15, 15) + 15*binomial(n/2+7, 7))/16 for even n.

%t A363350[n_]:=(Binomial[n+15,15]+If[EvenQ[n],15Binomial[n/2+7,7],0])/16;Array[A363350,50,0] (* _Paolo Xausa_, Nov 18 2023 *)

%o (PARI) a(n) = (binomial(n+15,15) + if(n%2==0, 15*binomial(n/2+7, 7)))/16

%Y Column k=4 of A362905.

%Y Cf. A006382.

%K nonn,easy

%O 0,3

%A _Andrew Howroyd_, May 30 2023